Germany were the first team to book their Euro 2012 place, winning all 10 of their qualification matches.
The Germans will be based in north Poland, but will travel to the Ukraine for all three of their group games.
They face Portugal in Lviv on Saturday June 9, Holland in Kharkiv on Wednesday June 13, then finish against Denmark in Lviv again, on Sunday June 17.
The Germans hammered Holland 3-0 in Hamburg last month in a friendly, but Löw said there would be no easy games in the group, although there was no fear of Portugal, who Germany beat 3-2 in the quarter-finals of Euro 2008.
"We'll take it as it comes, we have no fear," said Löw. "Before the draw, I said that there was no team I preferred to meet, everyone will be hard to play against.
"Being at a European Championships is just like being at a World Cup, any team can pull off a surprise."
The 51-year-old said he was also looking forward to facing World Cup finalists Holland, but that European neighbours Denmark would be especially dangerous.
"I believe that this is the heaviest and most balanced group with the strongest teams," said Löw.
"The Netherlands and Portugal have world-class players and we can look forward to interesting games against them.
“Denmark are always an uncomfortable team to face in a tournament.
"The Danes can assume the role of underdogs and take on bigger teams without pressure or fear. That makes them dangerous."
Having reached the final of Euro 2008 and finished third at last year's World Cup, Germany are one of the teams widely tipped to take the title in the final at Kiev's Olympic Stadium on July 1, but Löw dismissed the favourites tag.
"Before a tournament, a lot is always said, especially when people look at the qualification results," said Löw, who has coached Germany since 2006.
"But everyone knows that the title can only be won by the team in top form at the right time and when everything works.
"There is still a half year before the Euros and a lot can still happen - injuries for example.
"If we are in top form, we have a good chance, but that is also valid for Spain, who everyone has to be measured against, and also Holland, who will be stronger than they were against us in Hamburg.
"Also England, France, Italy and Portugal will have their chances."
Germany will face flights of 750km to Lviv, twice, and 1,500km to Kharkiv, but Löw says the travelling will be no worse than his team have already experienced.
"You have to fly anyway. Perhaps we will play the quarters or semi-final in Poland," said Löw.
"We were based in Switzerland for Euro 2008, but ended up flying to the final in Vienna."